Answer:
Δ QRS is an obtuse triangle ⇒ according to its angle
Δ QRS is an isosceles triangle ⇒ according to its sides
Step-by-step explanation:
In Δ QRS
∵ m∠Q = 8x - 17
∵ m∠R = 19x + 4
∵ m∠S = 5x + 1
→ The sum of the interior angles of a Δ is 180°
∴ m∠Q + m∠R + m∠S = 180°
→ Substitute their values in the equation above
∵ 8x - 17 + 19x + 4 + 5x + 1 = 180
→ Add the like terms
∴ (8x + 19x + 5x) + (-17 + 4 + 1) = 180
∴ 32x + (-12) = 180
∴ 32x - 12 = 180
→ Add 12 to both sides
∵ 32x - 12 + 12 = 180 + 12
∴ 32x = 192
→ Divide both sides by 32
∵ =
∴ x = 6
→ Substitute the value of x in each measure of angles to find them
∵ m∠Q = 8(6) - 17 = 48 - 17
∴ m∠Q = 31°
∵ m∠R = 19(6) + 4 = 114 + 4
∴ m∠R = 118°
∵ m∠S = 5(6) + 1 = 30 + 1
∴ m∠S = 31°
∵ m∠R > 90°
∴ ∠R is an obtuse angle
∴ Δ QRS is an obtuse triangle
∵ m∠Q = m∠S
→ In any Δ if two angles are equal in measures, then the two sides
opposite to these angles are equal in length and the Δ is isosceles
∴ RQ = RS
∴ Δ QRS is an isosceles triangle
Answer:
6n+2
Step-by-step explanation:
If n represents the number, the product of 6 and the number is the product of 6 and n: 6n.
When a quantity is "increased by 2" it means 2 has been added to it.
6n "increased by 2" is 6n+2
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = x - 9 ← is in slope- intercept form
with slope m =
• Parallel lines have equal slopes, hence
y = x + c ← is the partial equation of the parallel line.
To find c substitute (- 8, - 18) into the partial equation
- 18 = - 6 + c ⇒ c = - 18 + 6 = - 12
y = x - 12 ← equation of parallel line
Answer:
$4
Step-by-step explanation:
Given that
total cost of 8 identical pens and 2 identical files is $32
And, the The total cost of 3 such files would be the same as the total cost of 4 such pens
We need to find out the cost of each file
So let us assume the following things
Pens be x
File be y
Now
8x + 2y = $32 ....(1)
3y = 4x.........(2)
y = 4x÷ 3
Now put the value of y in equation 1
8x + 1.33x = 32
x = $3.55
x = $4
Answer:
Below in bold.
Step-by-step explanation:
You would join the faces with the greatest area
That is the faces with dimensions 3 feet by 5 feet.